Methods for Local Recovery of Tectonic Stresses Based on Kinematic Data: Physical Inconsistency and False Objectives. Part I

This work criticizes the entrenched views according to which the orientation of the principal tectonic stress axes can be determined from local (in time and space) observations of the kinematic indicators which jointly allow estimating the strain rate of a crustal block under study. The criticized approach ignores or replaces by subjective assumptions the following factors: (1) The block’s interaction with a hosting medium expressed in terms of the equilibrium conditions of the block; (2) The stress rate which (in addition to stresses) can affect the strain rate; (3)The specific macroscopic mechanical properties of the block’s material under the unknown sought stresses, including the ratio of the stress relaxation time to the period of observations. This approach, which is developed in some Solid Earth sciences and mainly in tectonophysics, is referred to in our paper as the method of local kinematic reconstruction (MLKR) of stresses. After briefly surveying the concept of forces and stresses and discussing the importance of studying the tectonic stresses, this paper refutes the MLKR notions based on general arguments and by the example of certain thought experiments. It is shown that the use of the MLKR for the conditions of the Earth’s interior does not guarantee against obtaining the results that fundamentally and drastically differ from the true tectonic stresses. In the studied rock block, depending on the factors ignored in the MLKR, the principal axes of the strain rate tensor, on one hand, and the principal stress axes, on the other hand, can be oriented discordantly in any arbitrary given fashion. In particular, in the processes accompanied by the release of elastic energy, the maximal rate of elongation can be oriented along the axis of maximal compression, whereas the maximal rate of shortening can be aligned with the axis of the maximal tension. In this paper, the deformation processes that are most detrimental to the results of stress reconstruction by the MLKR are revealed. We introduce the notion of the inherited stress-state regime in which the orientation of the axes of principal stresses during the observation period does not depend on the deformation process and, hence, cannot be in principle determined by the MLKR. An attempt to directly locally recover the stress axes from the kinematic data is a false objective because neither the physical meaning of the stress tensor nor the way it is introduced has anything to do with strains. It is concluded that the MLKR is physically inadequate and that the tectonophysical concept of locality should be abandoned in favor of returning to the notions of classical physics, namely, to using the conservation laws. By the example of several guides on tectonophysics, this paper exposes typical errors in understanding the stress reconstruction problem.     

西沙群岛石岛浅部基底地壳应力测量及其地球动力学意义分析

西沙群岛独特的构造位置决定了其构造运动背景和地壳应力场动力源的复杂性.位于西沙群岛石岛、深达1268.07m的西科1A井在1257.52m钻遇花岗岩基底.在1125.8~1262.0m开展5次水压致裂地应力测量,获得最大水平主应力为17.09~20.85MPa,最小水平主应力为15.97~18.29MPa,估算垂直主应力为22.86~26.68 MPa,地壳应力结构为SVSHSh,以垂直主应力为主导,该应力结构特征有利于正断层活动,表明西沙群岛地壳基底处于拉张的应力环境.受西沙海槽断层影响,水平应力值较低.印模测试显示基底地壳应力方向以近东西-北西向为主,与已有的GPS测量、横波分裂和面波反演结果较为吻合,显示西沙群岛岩石圈尺度上变形一致性较好.西沙群岛地壳应力场的力源受板块运动和地幔物质上涌作用联合制约.综合南海西北部实测地应力数据分析,显示该区域主应力方向较为一致,应处于统一、稳定的构造运动背景之中.西科1A井水压致裂试验是我国首次涉海深孔地壳应力测量,具有重要的地球动力学意义,提供了研究南海地球物理场的宝贵基础资料.     

山西煤矿矿区井下地应力场分布特征研究

采用煤矿井下专用的小孔径水压致裂地应力测量装置,在山西省的晋城、潞安、汾西、华晋、阳泉、平朔、大同等矿区,完成了160个测点的地应力测量,测点地质条件涵盖了山西省煤矿大部分条件.基于实测数据,分析了地应力与测点埋深的关系,不同深度条件下煤矿矿区井下地应力状态;绘制出山西省煤矿矿区井下地应力分布图,并与震源机制解的分析结果进行了比较,得出山西省煤矿矿区井下地应力场分布特征与变化规律.煤矿井下水平应力总体上随着埋深增加而增大,但由于各矿区地质条件差异较大,导致地应力测试数据离散性也较大;埋深小于250 m的岩层应力状态主要为σ_H>σ_h>σ_V型,埋深处于250~500 m的岩层应力状态以σ_H>σ_V>σ_h型为主,埋深较大的矿区主要为σ_V>σ_H>σ_h型;最大水平主应力与垂直主应力的比值绝大部分集中在0.5~2.0之间,而且随着埋深增加,侧压比呈现减小的趋势,并向1附近集中;最大水平主应力与最小水平主应力的比值主要集中在1.5～2.0之间;平均水平主应力与垂直主应力的比值大多处于0.5～1.5,尤以0.5～1.0之间最多;山西省煤矿矿区从北到南,最大水平主应力方向发生了较大变化.北部最大水平主应力方向为NE,往南发生偏转到NNW;靠东部与西部偏向NW;靠东南部出现了多变的方向.井下实测数据与震源机制解相比在部分区域一致性较好,而在另一些区域存在明显的差异.特别是在受较大地质构造影响的区域,水平主应力方向往往发生明显的扭转和变化.     

Field of tectonic stresses from focal mechanisms of earthquakes and recent crustal movements from GPS measurements in China

Orientations of the principal axes of the tectonic stress field reconstructed from seismological data on focal mechanisms of earthquakes and strain fields determined from GPS measurements in China are compared. The data of GPS measurements used in the paper were obtained by the Crustal Movement Observation Network of China (about 1000 stations) in the period of 1998–2004. On the basis of information on the recent horizontal crustal motions, the strain field is calculated for the study territory by the finite element method. Calculations of the strain tensor using GPS data were carried out with a step of 1° in latitude and longitude. A catalog of earthquake focal mechanisms was used for the reconstruction of tectonic stress field components. Focal mechanisms of earthquakes were calculated with the use of seismological data on signs of first arrivals from the bulletin of the International Seismological Center. To estimate characteristics of the regional stress field, an approach based on the kinematic method proposed by O.I. Gushchenko was applied. The tectonic stress field was reconstructed in depth intervals of 0 < H < 35 km and 35 km < H < 70 km from data on focal mechanisms of earthquakes over the periods of 1998–2004 and 1985–2004. Comparison of directions of the principal strain axes at the surface (according to GPS measurements) and directions of the principal stress axes (reconstructed from focal mechanisms of earthquakes) showed their good convergence. Seismotectonic strains and GPS measurements coincide within a larger part of the territory. The coincidence is best in a depth interval of 0 < H < 35 km. Maximum misfit values are confined to areas of high 3-D gradients of strain axis directions and are possibly related to the structural heterogeneity of the region, zones with strains of the same type along both horizontal axes (compression or extension along all directions), or areas of small absolute values of recent horizontal movements. Areas with invariable directions of the stress axes are recognizable regardless of the depth of initial data. Good reproducibility of results obtained by two different methods made it possible to check the method of stress field reconstruction using data on focal mechanisms of earthquakes.     

The global stress field in the lithosphere obtained from the satellite gravitational harmonics

In this paper, the lithosphere is considered to be a homogeneous elastic spherical shell for the sake of simplicity and the stress equations for the base of the lithosphere are taken as boundary conditions. Then the stress equations are obtained for use in the computation of the stress field in the lithosphere with the satellite gravitational harmonic coefficients. The 5 × 5° global stress field in the lithosphere is computed from harmonics of 2–30°. The directions of principal stresses of this stress field agree favourably with the directions of principal stresses indicated by mid-plate earthquake mechanisms, in situ stress measurements and sensitive geological features. This result indicates that the drag forces exerted on the base of the lithosphere, due to gravitational mantle convection, may be among the driving forces of plate motion and a major source for the stress field in the lithosphere.     

Principal horizontal stresses in Southern Africa

A review ofin situ stress measurements at eight regional localities in Africa south of the 15°S parallel shows that average directions of the horizontal pricipal stresses are N-S and E-W. These directions agree with principal stress orientations deduced from earthquake fault plane solutions. However, the maximum and minimum principal horizontal stresses are not consistently oriented parallel to either the N-S or E-W direction; they may vary within an individual region because of local geological structures and from region to region. At the sites within the Witwatersrand sediments (all at depths greater than 500 m) the maximum stress tends to lie NW-SE but at three of the four sites outside the Witwatersrand sediments (all at depths less than 500 m) this stress is oriented approximately N-S.The data reported here are compared with horizontal stresses predicted for Southern Africa bySolomon, Sleep andRichardson (1975) from various plate tectonic driving force models. The agreement between orientations is fair for all sites but only the deép sites in the Witwatersrand sediments have comparable stress magnitudes.     

基于构造超压的地层压力预测方法研究

Traditional formation pressure prediction methods all are based on the formation undercompaction mechanism and the prediction results are obviously low when predicting abnormally high pressure caused by compressional structure overpressure. To eliminate this problem, we propose a new formation pressure prediction method considering compressional structure overpressure as the dominant factor causing abnormally high pressure. First, we establish a model for predicting maximum principal stress, this virtual maximum principal stress is calculated by a double stress field analysis. Then we predict the formation pressure by fitting the maximum principal stress with formation pressure. The real maximum principal stress can be determined by caculating the sum of the virtual maximum principal stresses. Practical application to real data from the A1 and A2 wells in the A gas field shows that this new method has higher accuracy than the traditional equivalent depth method.     

SEISMIC MEASUREMENTS FOR SAFETY IN MINES*

The study of rock stresses and their changes is of great importance for safety in mines. To detect dangerous stress accumulations in coal mines an empirical method, Jahn's drilling test, is generally used. An experimental survey to solve the same problem by geophysical measurements was undertaken in a Hungarian coal mine. The basic idea was to determine the easily measurable seismic velocities instead of the more difficult to measure stresses in the rocks, since there is a monotonic relation between them. During the survey seismic transmission-type measurements were carried out in the fore-field of longwall faces between the top and tail roads. The seismic velocity data obtained were processed using an iterative algebraic reconstruction technique to determine the ‘velocity field’, i.e., the seismic velocity distribution, of the area covered by the ray paths. By periodically repeating the measurements in the same area, it was possible to follow the changes in the stress conditions caused by mining operations.     

Direct time-domain soil profile reconstruction for one-dimensional semi-infinite domains

We discuss the inverse medium problem associated with the reconstruction of the heterogeneous material profile of a semi-infinite (layered) soil medium, directly in the time domain, based on the complete waveform response of the medium to interrogating waves. To tackle the inversion process, we use a partial-differential-equation-constrained optimization approach, supplemented with a time-dependent regularization scheme. We introduce an absorbing boundary to truncate the semi-infinite extent of the physical domain, and propose two schemes to refine the reconstructed profiles: the first is based on iteratively re-positioning the truncation boundary until convergence, and the second is based on optimizing the observation period, so as to exclude records with information beyond the truncation boundary. We present numerical results that attest to the efficacy of the proposed schemes in reconstructing sharp profiles of semi-infinite soil domains using both noise-free and noisy data, while in the presence of absorbing boundaries.     

Preliminary stress measurements in central California using the hydraulic fracturing technique

Use of the hydraulic fracturing technique for determiningin situ stress is reviewed, and stress measurements in wells near the towns of Livermore, San Ardo, and Menlo Park, California are described in detail. In the Livermore well, four measurements at depths between 110 and 155 m indicate that the least principal compressive stress is horizontal and increases from 1.62 to 2.66 MPa. The apparent direction of maximum compression is N 70° E (±40°). At the San Ardo site the least principal stress is that due to the overburden weight. At depths of 240.2 and 270.7 m the minimum and maximum horizontal stresses are estimated to be 11.4 and 22.5 MPa, and 12.0 (±1.1) and 15.8 (±3.3) MPa, respectively. From an impression of the fracture at 240.2 m, the direction of maximum compression appears to be about N 15° E. The rock in the Menlo Park well is too highly fractured to yield a reliable measurement of the horizontal stresses. The data indicate, however, that the least principal stress is vertical (due to the overburden weight) to a depth of 250 m.     

Propagation of plane waves in an unbounded elastic medium with Cauchy's initial stress

Summary Cauchy theory of initial stress has been applied to investigate the influence of uniform initial stress on the propagation of plane waves in an unbounded elastic medium. It is found that if the initial principal stresses are unequal, the velocity depends on the direction in which the wave propagates, whereas when the initial principal stresses are equal, the velocity is independent of the direction of wave propagation.     

A model for the 3D kinematic interaction analysis of pile groups in layered soils

The paper presents a numerical model for the analysis of the soil–structure kinematic interaction of single piles and pile groups embedded in layered soil deposits during seismic actions. A finite element model is considered for the pile group and the soil is assumed to be a Winkler‐type medium. The pile–soil–pile interaction and the radiation problem are accounted for by means of elastodynamic Green's functions. Condensation of the problem permits a consistent and straightforward derivation of both the impedance functions and the foundation input motion, which are necessary to perform the inertial soil–structure interaction analyses. The model proposed allows calculating the internal forces induced by soil–pile and pile‐to‐pile interactions. Comparisons with data available in literature are made to study the convergence and validate the model. An application to a realistic pile foundation is given to demonstrate the potential of the model to catch the dynamic behaviour of the soil–foundation system and the stress resultants in each pile. Copyright © 2009 John Wiley & Sons, Ltd.     

Embedded foundation in layered soil under dynamic excitations

The critical step in the substructure approach for the soil–structure interaction (SSI) problem is to determine the impedance functions (dynamic-stiffness coefficients) of the foundations. In the present study, a computational tool is developed to determine the impedance functions of foundation in layered soil medium. Cone frustums are used to model the foundation soil system. Cone frustums are developed based on wave propagation principles and force-equilibrium approach. The model is validated for its ability to represent the embedded foundation in layered medium by comparing the results with the rigorous analysis results. Various degrees of freedom, such as, horizontal, vertical and rocking are considered for this study.     

Regional flow simulation in fractured aquifers using stress-dependent parameters

A model function relating effective stress to fracture permeability is developed from Hooke's law, implemented in the tensorial form of Darcy's law, and used to evaluate discharge rates and pressure distributions at regional scales. The model takes into account elastic and statistical fracture parameters, and is able to simulate real stress-dependent permeabilities from laboratory to field studies. This modeling approach gains in phenomenology in comparison to the classical ones because the permeability tensors may vary in both strength and principal directions according to effective stresses. Moreover this method allows evaluation of the fracture porosity changes, which are then translated into consolidation of the medium.     

Underground Measurements of Electromagnetic Radiation Related to Stress-induced Fractures in the Odenwald Mountains (Germany)

The regional stress field at Wald-Michelbach (Odenwald Mountains, Germany) induces a secondary stress field around the space of the local railway tunnel. Resulting maximum shear stresses produce microfractures, which emit electromagnetic radiation (EMR). From EMR measured along the cross section and the long axis of the tunnel, the regional stress field is determined by a correlation of detected impulses per time with stresses calculated from the orientation of the tunnel, its diameter, and topographic load. The major horizontal principal stress has an azimuth of 103°. At times, strongly alternating EMR values are observed, which indicate electromagnetic disturbances of unknown origin. Such disturbances are identified by repeated measurements and are not evaluated. The repeated measurements, which are not disturbed, differ with median 112 impulses per 100 ms. This difference corresponds to 0.037 MPa and indicates a good reproducibility of the results. Regional stress magnitudes and the WNW-ESE orientation of the major horizontal principal stress indicate a minor N – S directed tensional force at the western shoulder of the Upper Rhine Graben.     

Tectonic stress accumulation in the region of the Kuril–Kamchatka Island Arc system

The time variations in the tidal response of the medium in 2011–2015 according to the measurements at the global seismographic network (GSN) in Kamchatka are considered. Based on the data from the horizontal pendulums recording the eastward tilts at the station, it is established that there was a linear growth in the tidal tilt amplitudes up to May 24, 2013 due to the changes in the elastic moduli caused by tectonic stress accumulation. The growth phase was followed by the decline in the tidal tilt amplitudes induced by the release of stresses after the Sea-of-Okhotsk earthquake.     

Transhorizon propagation of decameter waves

Solutions to the problem of the point source field in a spherically layered medium are analyzed. For a three-layer waveguide model, a solution in the form of the Watson integral was used. A consideration of the singularities in the plane of the integration variable made it possible to represent the integral as a superposition of three waves. Two of them are connected with the interaction of the primary spherical wave with the lower convex and upper concave interfaces. The third wave is connected with the alternate action with both interfaces. The fourth wave is caused by the interaction between the primary wave and random inhomogeneities of the external medium (the ionosphere). Here, simulation was carried out based on Green equations. The considered unique data of flight measurements of the point source field strength indicate the efficiency of simulating the transhorizon propagation of decameter waves based on the superposition of all four aforesaid wave packets.     

Northeast-southwest compressive stress in Alberta evidence from oil wells

The introduction of the four-arm dipmeter well-logging tool has permitted hole asymmetry to be recognised and hole ellipticity to be measured and oriented. Many wells in Alberta, western Canada, have been shown to exhibit depth ranges over which they are non-circular as a result of caving of their walls. These break-outs occur so as to elongate the holes in a northwest-southeast direction. This direction of elongation is consistent between the break-outs in a given well, and between wells distributed over an area of more than 3 × 10⁵ km². Asymmetric hole elongation occurs in siltstones, sandstones, limestones, dolomites and one shale formation, and through the stratigraphic column from Devonian to Cretaceous. It is unrelated to dip of the strata. The hypothesis is advanced that the break-outs are caused by concentration of stress at the walls of the wells, in a stress field with large, unequal horizontal principal stresses, the larger oriented NE-SW. It is shown that a normal stress field (with the largest principal stress, σ₁, vertical) is unlikely to produce large enough horizontal stresses to produce the break-outs. Consequently our hypothesis requires σ₁ to be horizontal and oriented NE-SW. The vertical principal stress could be either σ₂ (strike-slip stress field) or σ₃ (thrust stress field). The orientation of σ₁ at right angles to the Rocky Mountains fold axes suggests the possibility that the stress field responsible for the thrust faulting in the mountains is still present. A strike-slip stress field is also possible. The most prominent system of surface joints outcropping in Alberta, shown by Babcock to have sets oriented NE-SW and NW-SE, could have been formed in the proposed stress field. Direct measurements of the stress tensor at two or three points, if they verified this interpretation, would combine with the oil well break-outs to demonstrate a remarkably uniform stress field over a substantial part of the North American plate. The stresses in the Alberta crust here proposed may be related to tractions now acting on the edges and underside of the North American plate, including those producing postglacial uplift of Hudson's Bay; or may be residual stresses from past tectonic events such as the Laramide compression of the Rocky Mountains.     

The effect of a deviatoric stress on physical rock properties

Petrophysical measurements were carried out on dry specimens of mica-gneiss, amphibolite and serpentinite from KTB core samples and samples of surface outcrops in order to determine the effect that a deviatoric stress field, as observed at the KTB area, may have on the in-situ rock properties. Simulating the variation of the actual principal stresses and temperature with depth, seismic wave velocities, densities, linear and volumetric strain (porosity) have been measured, taking into account the overall spatial orientation of the foliation at the KTB area with respect to the principal stress axes. Comparison with respective data evaluated for lithostatic pressure conditions revealed that the stress-related (crack-related) effect on wave velocities respectively on velocity anisotropy is in the range 1–3%, due to microcracks which are selectively closed or kept open by the deviatoric stress. The effect of the deviatoric stress is particularly documented by shear wave splitting due to microfractures that are oriented normal to the minimum principal stress axis.     

Syntheses of the regional stress fields of the Japanese islands

The principal stresses in northern Honshu and in central-southwest Japan are synthesized on the basis of the ridge push, slab pull and across-arc variation of differential forces due to crust/plate structural variation. Assuming a more compressive north–south horizontal stress in central Japan-northern Honshu than that of southwest Japan, the calculated principal stress profiles explain the observed stress fields in these areas: namely, a strike–slip fault type for southwest-central Japan and a reverse fault type for northern Honshu, both having east–west σ_Hmax. Kyushu is characterized by the gradient of horizontal stresses both in the east–west and north–south directions, which cannot be explained by simple plate interactions or by crust/plate structural variation. Combined with other lines of evidence for existence of mantle upwelling in the East China Sea west of Kyushu, it is proposed that the stress gradient is produced by the viscous drag exerted by the flow spread laterally from the upwelling plume. The eastward movement of Kyushu and southwest Japan relative to Eurasia revealed by the recent Global Positioning System measurements conducted by the Geographical Survey Institute of Japan would be partly explained by this basal drag.